“HTC is undervalued and there is an opportunity for growth,” Mr. Simon said in response to questions. HTC didn’t immediately respond to a request for a comment on the stake buy.

But the stock purchase by Mr. Lai, who is known as an outspoken critic of China’s top leadership, suggests HTC could soon face more activist shareholders as investors seek changes in the firm that has been struggling to reverse sliding sales.

HTC’s investors have been calling for changes in the company’s management and operations, after it tumbled from the top of the U.S. smartphone market in 2011 to its first net loss on record in the third quarter this year. HTC’s stock has lost more than 85% of its value since its peak in April 2011, and closed at 144.0 New Taiwan dollars ($4.89) on Friday.

It has yet to be seen if Mr. Lai, a grade-school dropout with a rags-to-riches story, will become an activist investor who will push for changes at HTC.

“(It’s) no secret that Mr. Lai is active in the Taiwan market and no secret he has opinions,” Mr. Simon said.

Mr. Lai founded Next Media Ltd., which publishes the Apple Daily newspapers in Hong Kong and Taiwan. His company is well known for its muckraking reporting and also for its news animations business Next Media Animation, which makes satirical cartoons of public figures and news events.

Over the years, Mr. Lai has also been known as a shrewd investor, starting with his founding of the Asian clothing retail chain Giordano Ltd. in the 1980s.

For HTC, Mr. Lai’s interest could be good news, as it shows big-name investors still have faith in the company. HTC has recently taken steps to reassure investors that is trying to steady its business. HTC’s Chairwoman Cher Wang announced last month that she is becoming more involved in the company’s marketing and sales, as Chief Executive Peter Chou focuses on the company’s product development.

With Nokia Corp. selling its handset business to Microsoft Corp. this year and Blackberry Ltd. considering bids, analysts have said HTC should also consider merger options. But Ms. Wang has been adamant that the company is not for sale.